Hybrid algorithm for common best proximity points of some generalized nonself nonexpansive mappings

Abstract

© 2018 John Wiley & Sons, Ltd. In this paper, we first introduce a new class of generalized nonself nonexpansive mappings, called C-Berinde nonexpansive mappings, and study common best proximity point of two mappings in this class. We propose two hybrid algorithms for finding common best proximity points of two best proximally nonexpansive mappings for which one of them is C-Berinde nonself nonexpansive mapping. Strong convergence analysis of the proposed methods are discussed in a real Hilbert space. Moreover, we also give a numerical example to support our main results.